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Previous studies on social influence and virtual product adoption have mainly taken users’ purchase behavior as a dichotomous variable (i.e. purchasing or not). Given the prevalence of competing versions (basic vs upgraded) of a virtual product in online communities, this paper investigated the differences in the effect of social influence on users’ adoption of basic and upgraded choices of a virtual product. It also examined how the effect varies with users’ social status and user-level network density.

A natural experiment was conducted in an online game community. Two competing versions (basic vs upgraded) of a virtual product were provided for in-game purchase while a random set of users selected from 897,765 players received the notification of their friends’ adoption information. A competing-risk model was used to test the hypotheses.

Social influence exerts a stronger positive effect on users’ adoption of the upgraded virtual product than of the basic virtual product. Middle-status users have the greatest (least) susceptibility to social influence in adopting the upgraded (basic) virtual product than low- and high-status users. User’s network density enhances the effect of social influence on adoption of both virtual products, even more for the upgraded one.

This research contributes to the social influence and product adoption literature by disentangling the different effects of social influence on basic and upgraded versions of a virtual product. It also identifies the boundary conditions that social influence works for each version of the virtual product.

This study aims to propose a refined dynamic network slacks-based measure (DNSBM) to evaluate the efficiency of China's regional green innovation system which consists of basic research, applied research and commercialization stages and explore the influencing factors of the stage efficiency.

A two-step procedure is employed. The first step proposes an improved DNSBM model with flexible settings of stages' input or output efficiency and uses second order cone programming (SOCP) to solve the non-linear problem. In the second step, least absolute shrinkage and selection operator (LASSO) and Tobit models are used to explore the influencing factors of the stage efficiency. Global Dynamic Malmquist Productivity Index (GDMPI) and Dagum Gini coefficient decomposition method are introduced for further discussion of the productivity change and regional differences.

On average, Chinese provincial green innovation efficiency should be improved by 24.11% to become efficient. The commercialization stage outperforms the stages of basic research and applied research. Comparisons between the proposed model and input-oriented, output-oriented and non-oriented DNSBM models show that the proposed model is more advanced because it allows some stages to have output-oriented model characteristics while the other stages have input-oriented model characteristics. The examination of the influencing factors reveals that the three stages of the green innovation system have quite diverse influencing factors. Further discussion reveals that Chinese green innovation productivity has increased by 39.85%, which is driven mainly by technology progress, and the increasing tendency of regional differences between northern and southern China should be paid attention to.

This study proposes an improved dynamic three-stage slacks-based measure (SBM) model that allows calculating output efficiency in some stages and input efficiency in the other stages with the application of SOCP approach. In order to capture productivity change, this study develops a GDMPI based on the DNSBM model. In practice, the efficiency of regional green innovation in China and the factors that influence each stage are examined.